The diagonal of the axial cylinder is 10 cm, the radius of the base is 3 cm. Find the area of the lateral surface of the cylinder.
| August 23, 2021 | education
Determine the diameter of the circle at the base of the cylinder.
D = АD = 2 * R = 2 * 3 = 6 cm.
The axial section of the cylinder is rectangle ABCD.
Then, in the right-angled triangle ACD, according to the Pythagorean theorem, we define the leg CD, which is the height of the cylinder.
CD ^ 2 = AC ^ 2 – AD ^ 2 = 100 – 36 = 64.
CD = 8 cm.
Determine the circumference of the cylinder.
L = 2 * π * R = 2 * π * 3 = 6 * π see.
Let us determine the area of the lateral surface of the cylinder.
Sside = L * СD = 6 * π * 8 = 48 * π cm2.
Answer: The lateral surface area is 48 * π cm2.
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